2.3. Attributes with steering
2.3.1. Curvature
returns curvature properties from a steering cube
A local surface is constructed at the evaluation point by following the dip information from the steering cube. The curvature attribute specified in Output is then calculated according to Roberts (2001). In his Feb. 2001 First Break article, Roberts defines curvature as a two-dimensional property of a curve that describes how bent a curve is at a particular point in the curve, i.e. how much the curve deviates from a straight line. The same concept is used to describe the curvature of a surface. Curvature is measured on the curve which is the intersection between a plane and the surface. Since this can be done in numerous ways there is an infinite number of curvature attributes that can be calculated for any plane. The subset implemented here relates to the most useful subset of curvatures that are defined by planes that are orthogonal to the surface and which are called normal curvatures. A positive curvature corresponds to an anticline and a negative curvature indicates a syncline. A flat plane has zero curvature. The application suggestions are from Roberts (First Break, Feb 2001).
The curvature options in OpendTect are shown below.
2.3.1.1. Mean curvature
The average of any two orthogonal normal curvatures through a point on the surface is constant and is defined as the mean curvature. Minimum and Maximum curvature (see below) are orthogonal surfaces hence the mean curvature is also the sum of minimum and maximum curvature divided by two. The mean curvature is not considered a very important attribute for visualization purposes but it is used to derive some of the other attributes.
2.3.1.2. Gaussian curvature
The Gaussian curvature is defined as the product of the minimum and maximum curvature. It is sometimes referred to as the total curvature. The Gaussian curvature is not considered a very important attribute for visualization purposes but it is used to derive some of the other attributes.
2.3.1.3. Maximum curvature
From the infinite number of normal curvatures there exists one curve, which defines the largest absolute curvature. This is called the maximum curvature. The plane in which maximum curvature is calculated is orthogonal to the plane of the minimum curvature. This attribute is very effective at delimiting faults and fault geometries.
2.3.1.4. Minimum curvature
The minimum curvature is the smallest absolute curvature from the infinite number of normal curvatures that exist. The plane in which minimum curvature is calculated is orthogonal to the plane of the maximum curvature. The minimum curvature is often quite noisy but it can sometimes be diagnostic in identifying fractured areas. Moreover, it is used to compute other curvature attributes.
2.3.1.5. Most positive curvature
The most positive curvature returns the most positive curvature from the infinite number of normal curvatures that exist. The attribute reveals faulting and lineaments. The magnitude of the lineaments is preserved but the shape information is lost. This attribute can be compared to first derivative based attributes (dip, edge and azimuth).
2.3.1.6. Most negative curvature
The most negative curvature returns the most negative curvature from the infinite number of normal curvatures that exist. The attribute reveals faulting and lineaments. The magnitude of the lineaments is preserved but the shape information is lost. This attribute can be compared to first derivative based attributes (dip, edge and azimuth).
2.3.1.7. Shape index
The shape index ( Si ) is a combination of maximum and minimum curvature that describes the local morphology of the surface independent of scale. The attribute may reflect e.g. whether the surface corresponds to a bowl( Si=-1 ), a valley (Si=-1/2 ), ridge ( Si=+1/2 ), a dome ( Si=1 ) or it is flat ( Si=0 ). Because the attribute is not affected by the absolute magnitude of curvature it is reported to be useful for picking up subtle fault and surface lineaments as well as other patterns.
2.3.1.8. Dip curvature
The dip curvature returns the curvature of the intersection with the plane that defines the dip direction of the surface. This plane is orthogonal to the plane for the strike curvature. This curvature method tends to exaggerate local relief contained within the surface and can be used to enhance differential compacted features such as channeled sand bodies and debris flows.
2.3.1.9. Strike curvature
The strike curvature (also known as tangential curvature) returns the curvature of the intersection with the plane that defines the strike direction of the surface. This plane is orthogonal to the plane for the dip curvature. The attribute describes the shape of the surface. It is used extensively in terrain analysis, e.g. to study soil erosion and drainage patterns. The attribute reveals how shapes are connected, e.g. how ridges are connected to the flanks of anticlines. It may be useful for fluid-flow studies.
2.3.1.10. Contour curvature
The contour curvature (also known as plan curvature) is not a normal curvature. It is very similar to the strike curvature and effectively represents the curvature of the map contours associated with the surface. Contour curvature values are not very well constrained and large values can occur at the culmination of anticlines, synclines, ridges and valleys.
2.3.1.11. Curvedness
The Curvedness attribute describes the magnitude of curvature of a surface independent of its shape. The attribute gives a general measure of the amount of total curvature within the surface.
2.3.1.12. General Remark
Curvature can be used as input to other attributes. Especially the Volume Statistics attribute proves to give very useful outputs. Just select the curvature attribute as input and select the output statistic. For Fault Detection, the "Variance" is a suitable output statistic.
2.3.2. Dip
Returns dip/azimuth from a steering cube
Description. The inline, crossline dips of a steering cube are transformed to the requested Output type. When the steering cube was computed from seismic data sampled in time the dips in a steering cube are apparent dips (slowness) and the returned attribute will also represent apparent dips. To compute real dips, please use the dip angle attribute.
2.3.2.1. Polar dip
Converts the input orthogonal dips (inline and crossline dip) to the polar dip, or true dip. The dip is measured from the horizontal and the range of the dip is more than zero and given in usec/m.
2.3.2.2. Azimuth
Returns the Azimuth of the dip direction in degrees ranging from -180 to +180. Positive azimuth is defined from the inline in the direction of increasing crossline numbers. Azimuth = 0 indicates that the dip is dipping in the direction of increasing cross-line numbers. Azimuth = 90 indicates that the dip is dipping in the direction of increasing in-line numbers.
2.3.2.3. Inline dip
Returns the inline dip in usec/m.
2.3.2.4. Crossline dip
Returns the crossline dip in usec/m.
2.3.3. Dip angle
Returns the true dip from the apparent dip (slowness).
Description. Calculates the true dip from the apparent dip (slowness). If no velocity model is available, specify a constant velocity in the velocity field. The velocity should be given in meters per second.
2.3.4. Position
returns any attribute calculated at the location where an other attribute has its minimum, maximum or median within a small volume.
Description. The input attribute defines the attribute that is used to determine the position at which the output attribute has to be calculated. The stepouts, time gate and steering define the volume in which the input attribute is evaluated. The Operator determines which position is returned from this analysis; the position of the minimum, maximum or median of the input attribute. This position is the position at which the output attribute will be calculated.
For example, one can determine where in a small volume the energy is minimal, and output the frequency at the location of this lowest energy. Another way of applying this attribute is to output Median Dip Filtered data at minimum values in areas where faults are present. In this way, the noise is reduced and the faults are sharpened.
Steering. In Central Steering the local dip information at the reference point is followed from trace to trace until all samples in the specified search radius are found. Central steering thus collects the input values along a dipping plane. In Full steering the dip information of the reference point is used only to find the position (and value) of the adjacent trace. The dip information at this new position is then used to find the position (and value) of the next trace and so on, until all samples in the specified search radius are found. Full steering thus corresponds to collecting the input values along a curved surface. In Constant direction the steering information is user-specified. The range of the Apparent dip is more than zero, and the Azimuth is defined from the inline, in the direction of increasing crossline-numbers. The azimuth ranges from -180 to 180 degrees.
In all forms of steering the amplitude values at the intersection of trace and steering surface are determined by interpolation.
2.3.5. Reference shift
Moves the extraction position in 3D space.
Description. The Input attribute is extracted at the shifted position. Original reference (extraction) point has inline crossline co-ordinates (0,0). Relative number 1 means the next inline or crossline, respectively. The vertical shift is specified in ms using the Time option, or can be derived using steering. Steering is specified in one of the following ways:
None: the reference position is not shifted vertically.
Central: the reference position is vertically shifted according to the dip and azimuth information at (0,0,0) from the SteeringCube.
Full: the reference position is vertically shifted according to the dip and azimuth from the SteeringCube, from trace to trace from the starting position (0,0,0) to the position specified at Inl/Crl shift.
Constant direction: the reference position is vertically shifted according to a user defined Apparent dip and Azimuth.
Shifting the reference position is a form of directivity that is useful in multi-attribute analysis. For example, to highlight flat spots one may consider to train a neural network on attributes extracted in three horizontally aligned windows.
2.3.6. Similarity
Returns trace-to-trace similarity properties
Description. Similarity is a form of "coherency" that expresses how much two or more trace segments look alike. A similarity of 1 means the trace segments are completely identical in waveform and amplitude. A similarity of 0 means they are completely dis-similar. Consider the trace segments to be vectors in hyperspace. Similarity is then defined as the Euclidean distance between the vectors, normalized over the vector lengths. The trace segments as defined by the Time gate in ms and are found by Steering from the reference point to the specified Trace positions. Positions are specified in relative numbers (see figure). The Extension parameter determines how many trace pairs are used in the computation, see below.
Extension. With None specified, only the trace pairs specified in Trace positions are used to compute the output. Mirror at 90 degrees and Mirror at 180 degrees means that two similarities are computed: for the specified trace pair and for the pair that is obtained by 90 or 180 degrees rotation, respectively. The average, minimum or maximum of these pairs as specified in Output statistic is returned. In Full block all possible trace pairs in the rectangle defined by Inl/Crl stepout are computed. The statistical property specified in Output statistic is returned.
Steering. In Central Steering the local dip information at the reference point is followed from trace to trace until all samples in the specified search radius are found. Central steering thus collects the input values along a dipping plane. In Full steering the dip information of the reference point is used only to find the position (and value) of the adjacent trace. The dip information at this new position is then used to find the position (and value) of the next trace and so on, until all samples in the specified search radius are found. Full steering thus corresponds to collecting the input values along a curved surface. In Constant direction the steering information is user-specified. The range of the Apparent dip is more than zero, and the Azimuth is defined from the inline, in the direction of increasing crossline-numbers. The azimuth ranges from -180 to 180 degrees.
In all forms of steering the amplitude values at the intersection of trace and steering surface are determined by interpolation.
2.3.7. Volume statistics
Returns statistical properties from a small sub-volume
Description. The statistical property specified in Output statistic is returned. The input values are collected from a cube (rectangle) or cylinder (ellipsoid) around the reference point defined by parameters: Time gate, Shape and Inl/Crl stepout. Optionally Steering is used to obtain the trace segments of the input sub-volume.
Steering. In Central Steering the local dip information at the reference point is followed from trace to trace until all samples in the specified search radius are found. Central steering thus collects the input values along a dipping plane. In Full steering the dip information of the reference point is used only to find the position (and value) of the adjacent trace. The dip information at this new position is then used to find the position (and value) of the next trace and so on, until all samples in the specified search radius are found. Full steering thus corresponds to collecting the input values along a curved surface. In Constant direction the steering information is user-specified. The range of the Apparent dip is more than zero, and the Azimuth is defined from the inline, in the direction of increasing crossline-numbers. The azimuth ranges from -180 to 180 degrees.
In all forms of steering the amplitude values at the intersection of trace and steering surface are determined by interpolation.